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Chapter Cost Behavior: Analysis and Use Learning Objectives LO1 LO2 LO3 LO4 LO5 Understand how fixed and variable costs behave and how to use them to predict costs Use a scattergraph plot to diagnose cost behavior Analyze a mixed cost using the high-low method Prepare an income statement using the contribution format (Appendix 5A) Analyze a mixed cost using the least-squares regression method New in this Edition • Many new In Business boxes have been added • The end-of-chapter materials have been expanded by adding several new shorter exercises Chapter Overview A Types of Cost Behavior Patterns (Exercises 5-1, 5-6, 5-7, 5-8, 5-11, and 5-12.) At least three cost behavior patterns—variable, fixed, and mixed—are found in most organizations Of course, many other types of cost behavior patterns exist, but these three patterns are fairly common and the mixed cost model can be used to provide approximations to more complex cost behavior patterns within a relevant range It is important for managers to understand the behavior of each type of cost Variable Costs The total amount of a variable cost varies in direct proportion to changes in the activity level When expressed on a per unit basis, variable costs are constant Examples of costs that are normally variable with respect to output volume are listed in Exhibit 5-2 Be careful to point out to students that some of these costs may be fixed in some organizations This is particularly true of direct labor and other employee wages and salaries that may be effectively fixed due to labor laws in a country, custom, labor contracts, or the organization’s personnel policies Exhibit 5-8 in the text points out that in practice there is a wide variation in how some of these costs are classified by individual companies a Activity base (cost driver) For a cost to be variable, it must be variable with respect to some activity base An activity base is a measure of whatever causes the incurrence of a variable cost Some of the most common activity bases are machine-hours, units produced, and units sold A measure of activity should be used to allocate a cost for decision-making purposes only if it actually causes the cost b True variable and step-variable costs Some variable costs, such as direct materials, vary in direct proportion to the level of activity These costs are called true variable 267 costs A cost that is obtainable only in large chunks and that increases or decreases in response to fairly wide changes in the activity level is known as a step-variable cost For example, direct labor may be a step-variable cost when workers are only hired on a full-time basis The difference between a true variable and a step-variable cost is illustrated in Exhibit 5-3 in the text c In reality, many costs are curvilinear Most frequently, costs increase less than proportionately with activity Nevertheless, within any given narrow band of activity even a curvilinear cost function is approximately linear This narrow band of activity within which a particular straight line is a reasonable approximation to the true underlying cost function is called its relevant range • Thus, within the relevant range, variable cost per unit can be assumed to be constant Exhibit 5-4 in the text illustrates a curvilinear cost and the notion of the relevant range • The notion of the relevant range often causes confusion Some individuals refer to the relevant range as the range of activity within which the company expects to operate or has operated in the recent past That is not what we mean by the relevant range The relevant range, as we use the term, is the range of activity within which a particular straight line provides a reasonable approximation to the real underlying cost function Fixed Costs A fixed cost remains constant in total dollar amount within the relevant range Since fixed costs remain constant in total, the amount of cost computed on a per unit basis becomes smaller as the number of units produced increases Care must be exercised in interpreting fixed costs that have been expressed on a per unit basis; they should not be misinterpreted as variable costs a For planning purposes, fixed costs can be viewed as either committed or discretionary • Committed fixed costs Committed fixed costs relate to investment in buildings, equipment, and the basic organizational structure of a company Committed fixed costs are long-term and can’t be significantly reduced even for a short period of time without seriously impairing long-run goals • Discretionary fixed costs Discretionary fixed costs are those that management adjusts periodically Examples of discretionary fixed costs include advertising, research, and management development programs The planning horizon for discretionary fixed costs is fairly short—usually a single year Management may be able to adjust these fixed costs as circumstances change b The relevant range for a fixed cost is that range of activity over which total fixed cost does not change Exhibit 5-6 in the text illustrates this idea Mixed Costs A mixed cost contains both variable and fixed cost elements Many costs are mixed and can be expressed in terms of the cost formula Y = a + bX, where Y is the total estimated cost, a is the estimated total fixed cost, b is the estimated variable cost per unit of activity, and X is the amount of activity Even when the underlying cost is not linear, this formula can provide a reasonable approximation to the underlying cost function within the relevant range 268 Classification of costs A cost that is considered variable in one organization may be considered fixed in another due, for example, to differing employment policies Exhibit 5-8 in the text shows that there is a lot of variation in how companies classify costs in terms of behavior B Analysis of Mixed Costs For planning and control purposes, mixed costs should be broken down into variable and fixed components A number of methods can be used to analyze mixed costs Account analysis and the engineering approach are mentioned briefly in this chapter and are covered in more detail in later chapters This chapter discusses in more depth three techniques for analyzing past records of cost and activity—the scattergraph method, the high-low method, and least-squares regression The Scattergraph Method (Exercises 5-2, 5-9, and 5-10.) a The data should be plotted no matter what method is ultimately used to estimate fixed and variable costs A graph is constructed with cost on the vertical axis and activity on the horizontal axis Costs at various levels of activity are then plotted on the graph This plot will often provide important insights concerning the underlying relationship and can help in identifying nonlinearities and outliers (unusual points) that should be ignored b While this is not ordinarily done in practice, a line can be fitted to the plotted points by eye with a straightedge The line should be placed so that approximately equal numbers of points fall above and below it While not strictly necessary, in the text and in problems we always draw the line through one of the points to simplify calculations This line can then be used to derive what we call “quick-and-dirty” estimates of the fixed and variable costs The fixed cost can be estimated by the vertical intercept The variable cost per unit can be estimated by computing the slope of the line The High-Low Method (Exercises 5-2, 5-4, 5-7, 5-8, 5-9, and 5-11.) The high-low method of analyzing mixed costs focuses exclusively on the high and low levels of activity The difference in cost observed at these two extremes is divided by the change in activity to estimate the variable cost per unit of activity A major defect of the high-low method is that it utilizes only two points and ignores all of the other data Generally, two points are not enough to produce accurate results Moreover, the periods in which the high and low activity levels occur are often not typical of most periods The Least-Squares Regression Method (Exercises 5-3 and 5-12.) Using mathematical formulas, the least-squares regression method fits a regression line that minimizes the sum of the squared errors Exhibit 5-13 can be used as a basis for discussing the theory of leastsquares regression a We don’t go into the details of the computation of the least-squares regression estimates since computer software is widely used for performing this chore The appendix to the chapter shows how to use Excel to the necessary calculations b In addition to estimates of the slope (variable cost per unit) and the intercept (total fixed cost), least-squares regression software can produce a variety of informative 269 statistics One of the most informative is the R2, which is a measure of the goodness of fit of the regression line It tells us the percentage of the variation in the dependent variable (cost) that is explained by variation in the independent variable (activity) We not show in the text how the R2 is computed, but you may want to discuss its interpretation with students c Multiple regression analysis should be used when the cost is caused by more than one factor C The Contribution Format (Exercises 5-5 and 5-6.) Two major approaches can be used to prepare an income statement The difference between these two approaches centers on the way in which costs are organized The Traditional Approach The traditional approach to the income statement organizes data in a functional format, based on the functions of production, administration, and sales The emphasis is on the purposes for which the costs were incurred No attempt is made to identify the behavior of costs included under each functional heading This approach is used to prepare income statements for external reporting purposes The Contribution Approach The contribution approach to the income statement organizes costs by behavior, rather than by function a The contribution approach separates costs into fixed and variable categories Variable expenses are deducted to obtain the contribution margin Fixed expenses are then deducted from the contribution margin to obtain net operating income b The contribution approach to the income statement makes it much easier for managers to understand the relations between volume and expenses, and volume and profits Variable and fixed costs are not lumped together Since planning and decision-making often involve changes in the level of activity, contribution income statements can be very useful Unfortunately, the contribution approach is seldom used in practice 270 Assignment Materials Assignment Exercise 5-1 Exercise 5-2 Exercise 5-3 Exercise 5-4 Exercise 5-5 Exercise 5-6 Exercise 5-7 Exercise 5-8 Exercise 5-9 Exercise 5-10 Exercise 5-11 Exercise 5-12 Problem 5-13 Problem 5-14 Problem 5-15 Problem 5-16 Problem 5-17 Problem 5-18 Problem 5-19 Problem 5-20 Problem 5-21 Problem 5-22 Problem 5-23 Problem 5-24 Case 5-25 Case 5-26 Case 5-27 Case 5-28 Level of Topic Difficulty Fixed and variable cost behavior Basic High-low method; scattergraph analysis Basic (Appendix 5A) Least-squares regression Basic High-low method Basic Contribution format income statement Basic Basic Cost behavior; contribution format income statement High-low method; predicting cost Basic High-low method; predicting cost Basic Scattergraph analysis; high-low method Basic Scattergraph analysis Basic Basic Cost behavior; high-low method (Appendix 5A) Least-squares regression Basic Cost behavior; high-low method; contribution income statement Basic Basic Contribution format versus traditional income statement (Appendix 5A) Least-squares regression; scattergraph; cost behavior Basic Identifying cost behavior patterns Medium High-low and scattergraph analysis Medium (Appendix 5A) Least-squares regression method Medium Scattergraph analysis Medium (Appendix 5A) Least-squares regression method Medium (Appendix 5A) Least-squares regression analysis; contribution income statement Medium High-low method; cost of goods manufactured Difficult High-low method; predicting cost Difficult High-low method; predicting cost Difficult (Appendix 5A) Analysis of mixed costs, job-cost system, and activity-based costing Difficult Scattergraph analysis; selection of an activity base Medium Analysis of mixed costs in a pricing decision Difficult (Appendix 5A) Mixed cost analysis by three methods Difficult Suggested Time 15 45 30 20 20 20 30 20 30 30 20 30 45 45 45 30 45 30 30 30 45 45 45 45 90 45 90 90 Essential Problems: Problem 5-13, Problem 5-17 or Problem 5-19, Problem 5-23 or Problem 524 Supplementary Problems: Problem 5-14, Problem 5-16, Problem 5-22, Case 5-25, Case 5-26, Case 5-27, Case 5-28 Appendix 5A Essential Problems: Problem 5-15 Appendix 5A Supplementary Problems: Problem 5-18, Problem 5-20, Problem 5-21 Linked problems and exercises: Exercise 5-3 should be assigned in conjunction with Exercise 5-2 Exercise 5-9 should be assigned in conjunction with Exercise 5-8 Problem 5-18 should be assigned in conjunction with Problem 5-17 271 272 Chapter Lecture Notes Helpful Hint: The McGraw-Hill/Irwin Managerial/Cost Accounting video library does not contain a segment that relates to Chapter I Chapter theme: Managers who understand how costs behave are better able to predict costs and make decisions under various circumstances This chapter explores the meaning of fixed, variable and mixed costs (the relative proportions of which define an organization’s cost structure) It also introduces a new income statement called the contribution approach Types of cost behavior patterns A Variable costs i A variable cost is a cost whose total dollar amount varies in direct proportion to changes in the activity level An activity base (also called a cost driver) is a measure of what causes the incurrence of variable costs As the level of the activity base increases, the variable cost increases proportionally a Units produced (or sold) is not the only activity base within companies A cost can be considered variable if it varies with activity bases such as 273 274 5 miles driven, machine hours, or labor hours As an example of an activity base, consider your total long distance telephone bill The activity base is the number of minutes that you talk ii Variable costs remain constant if expressed on a per unit basis Referring to the telephone example, the cost per minute talked is constant (e.g., 10 cents per minute) iii Extent of variable costs The proportion of variable costs differs across organizations For example: a A public utility like Florida Power and Light, with large investments in equipment, will tend to have fewer variable costs b A manufacturing company like Black and Decker will often have many variable costs associated with the manufacture and distribution of its products to customers c A merchandising company like Wal-Mart will usually have a high proportion of variable costs such as the cost of merchandise purchased for resale d Some service companies, such as restaurants, have a high proportion of variable costs due to their raw 275 276 TM 5-2 VARIABLE COST BEHAVIOR Many costs can be described as variable, fixed, or mixed A variable cost changes in total in proportion to changes in activity; a variable cost is constant on a per-unit basis Total Cost of Bicycle Chains EXAMPLE: Each bicycle requires one bicycle chain costing $8 • $8 per bicycle chain $800 0 100 Number of Bicycles Produced © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-3 EXAMPLES OF COSTS THAT ARE NORMALLY VARIABLE WITH RESPECT TO OUTPUT VOLUME Merchandising company Costs of goods (merchandise) sold Manufacturing company Manufacturing costs: Prime costs: Direct materials Direct labor* Variable portion of manufacturing overhead: Indirect materials Lubricants Supplies Power Both merchandising and manufacturing companies Selling, general, and administrative costs: Commissions Clerical costs, such as invoicing Shipping costs Service organizations Supplies, travel, clerical *Whether direct labor is fixed or variable will depend on the labor laws of the country, custom, and the company’s employment contracts and policies © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-4 FIXED COST BEHAVIOR A fixed cost remains constant in total amount throughout wide ranges of activity EXAMPLE: Fashion photographer Lori Yang rents studio spaces in a prestige location for $50,000 a year She measures her company’s activity in terms of the number of photo sessions Cost Cost of Studio Rental $50,000 1,000 500 Number of Photo Sessions © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-5 FIXED COST BEHAVIOR (cont’d) A fixed cost varies inversely with activity if expressed on a per unit basis Average Cost Per Photo Session for Studio Rental $200 $160 $120 $80 $40 $0 500 1,000 Number of Photo Sessions © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-6 TYPES OF FIXED COSTS • Committed fixed costs relate to investment in plant, equipment, and basic administrative structure It is difficult to reduce these fixed costs in the short-term Examples include: • Depreciation on plant facilities • Taxes on real estate • Salaries of key operating personnel • Discretionary fixed costs arise from annual decisions by management to spend in certain areas These costs can often be reduced in the short-term Examples include: • Advertising • Research • Public relations • Management development programs TREND TOWARD FIXED COSTS The trend is toward greater fixed costs relative to variable costs The reasons for this trend are: • Increased automation of business processes • Shift from laborers paid by the hour to salaried knowledge workers © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-7 MIXED COSTS A mixed (or semi-variable) cost contains elements of both variable and fixed costs Example: Lori Yang leases an automated photo developer for $2,500 per year plus 2¢ per photo developed Y Slope = b Lease Cost $2,800 Variable Cost Element $2,500 Intercept = a Fixed Cost Element $0 5,000 10,000 15,000 Photos Developed Equation of a straight line: Y = a + bX Y = $2,500 + $0.02X © The McGraw-Hill Companies, Inc., 2006 All rights reserved X TM 5-8 MIXED COSTS (cont’d) A cost that is considered fixed in one company might be considered variable or mixed in another company © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-9 SCATTERGRAPH METHOD As the first step in the analysis of a mixed cost, the cost and its activity base should be plotted on a scattergraph This helps to quickly diagnose the nature of the relation between the cost and the activity base Example: Piedmont Wholesale Florists has maintained records of the number of orders and billing costs in each quarter over the past several years Number Quarter of Orders Year 1—1st 2nd 3rd 4th Year 2—1st 2nd 3rd 4th Year 3—1st 2nd 3rd 1,500 1,900 1,000 1,300 2,800 1,700 2,100 1,100 2,000 2,400 2,300 Billing Costs $42,000 $46,000 $37,000 $43,000 $54,000 $47,000 $51,000 $42,000 $48,000 $53,000 $49,000 These data are plotted on the next page, with the activity (number of orders) on the horizontal X axis and the cost (billing costs) on the vertical Y axis © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-10 A COMPLETED SCATTERGRAPH Y $60,000 Regression Line Billing Costs $50,000 $48,000 $40,000 $30,000 $20,000 $10,000 X $0 500 1,000 1,500 2,000 Number of Orders 2,500 3,000 The relation between the number of orders and the billing cost is approximately linear (A straight line that seems to reflect this basic relation was drawn with a ruler on the scattergraph.) Since a straight line seems to be a reasonable fit to the data, we can proceed to estimate the variable and fixed elements of the cost using one of the following three methods 1) Quick-and-dirty method based on the line in the scattergraph 2) High-low method 3) Least-squares regression method © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-11 THE QUICK-AND-DIRTY METHOD The straight line drawn on the scattergraph can be used to make a quick-and-dirty estimate of the fixed and variable elements of billing costs Recall that we are trying to estimate the fixed cost, a, and the variable cost per unit, b, in the linear equation Y= a + bX • The vertical intercept, approximately $30,000 in this case, is a rough estimate of the fixed cost • The slope of the straight line is an estimate of the variable cost per unit Select a point falling on the line (in this case 2,000 orders): Total billing cost for 2,000 orders Less fixed cost element (intercept) Variable cost element for 2,000 orders $48,000 30,000 $18,000 Variable cost per unit = $18,000 ÷ 2,000 orders = $9 per order Therefore, the cost formula for billing costs is $30,000 per quarter plus $9 per order or: Y = $30,000 + $9X, where X is the number of orders Because of the imprecision of this method of estimating the variable and fixed cost components of a mixed cost, it is seldom used in practice Nevertheless, it is always a good idea to plot the data on a scattergraph before using the more precise high-low or least-squares regression methods © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-12 ANALYSIS OF MIXED COSTS: HIGH-LOW METHOD EXAMPLE: Kohlson Company has incurred the following shipping costs over the past eight months: Units Sold January 6,000 February 5,000 March 7,000 April 9,000 May 8,000 June 10,000 July 12,000 August 11,000 Shipping Cost $66,000 $65,000 $70,000 $80,000 $76,000 $85,000 $100,000 $87,000 With the high-low method, only the periods in which the lowest activity and the highest activity occurred are used to estimate the variable and fixed components of the mixed cost High activity level, July Low activity level, February Change Variable cost= Units Sold 12,000 5,000 7,000 Shipping Cost $100,000 65,000 $ 35,000 Change in cost $35,000 = =$5 per unit Change in activity 7,000 units Fixed cost = Total cost - Variable cost element = $100,000 - (12,000 units × $5 per unit) = $40,000 The cost formula for shipping cost is: Y = $40,000 + $5X © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-13 EVALUATION OF THE HIGH-LOW METHOD Y high level of activity Shipping Costs $100,000 $80,000 low level of activity Variable Cost $5/unit $60,000 $40,000 Fixed Cost $40,000 $20,000 X $0 2,000 4,000 6,000 8,000 10,000 12,000 Units Sold The high-low method suffers from two major defects: It throws away all but two data points The high and low volume periods are often unusual © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-14 LEAST-SQUARES REGRESSION METHOD The least-squares regression method for analyzing mixed costs uses mathematical formulas to determine the regression line that minimizes the sum of the squared “errors.” © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-15 LEAST-SQUARES REGRESSION (cont’d) Example: Montrose Hospital operates a cafeteria for employees Management would like to know how cafeteria costs are affected by the number of meals served April May June July August September Meals Served X 4,000 1,000 3,000 5,000 10,000 7,000 Total Cost Y $9,500 $4,000 $8,000 $10,000 $19,500 $14,000 Statistical software or a spreadsheet program can the computations required by the least-squares method The results in this case are: Intercept (fixed cost) Slope (variable cost) R2 $2,433 $1.68 0.99 The fixed cost is therefore $2,433 per month and the variable cost is $1.68 per meal served, or: Y = $2,433 + $1.68X, where X is meals served R2 is a measure of the goodness of fit of the regression line In this case, it indicates that 99% of the variation in cafeteria costs is due to the number of meals served This suggests a very good fit © The McGraw-Hill Companies, Inc., 2006 All rights reserved TM 5-16 TRADITIONAL VERSUS CONTRIBUTION INCOME STATEMENT Traditional Approach (costs organized by function) Sales Less cost of goods sold* Gross margin Less operating expenses: Selling* Administrative* Net operating income Contribution Approach (costs organized by behavior) $60,000 34,000 26,000 $15,000 6,000 21,000 $ 5,000 Sales Less variable expenses: Variable production $12,000 Variable selling 3,000 Variable administrative 1,000 Contribution margin Less fixed expenses: Fixed production 22,000 Fixed selling 12,000 Fixed administrative 5,000 Net operating income $60,000 16,000 44,000 39,000 $ 5,000 * Contains both variable and fixed elements since this is the income statement for a manufacturing company If this were a merchandising company, then the cost of goods sold would be entirely variable © The McGraw-Hill Companies, Inc., 2006 All rights reserved
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